Question: Solve for $x$ : $x^2 - 14x + 40 = 0$
Explanation: The coefficient on the $x$ term is $-14$ and the constant term is $40$ , so we need to find two numbers that add up to $-14$ and multiply to $40$ The two numbers $-10$ and $-4$ satisfy both conditions: $ {-10} + {-4} = {-14} $ $ {-10} \times {-4} = {40} $ $(x {-10}) (x {-4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -10) (x -4) = 0$ $x - 10 = 0$ or $x - 4 = 0$ Thus, $x = 10$ and $x = 4$ are the solutions.